- NumPI - Mailing list — Dipartimento di Matematica, UniPI

Optimization & Numerical Analysis seminars: Sergeyev (II)
by Federico Poloni 24 Mar '16

24 Mar '16

Speaker: Yaroslav D. Sergeyev Affiliation: Università della Calabria and N.I. Lobachevsky University of Nizhni Novgorod, Russia. Time: Tuesday, 12 April 2016, 12:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: The Infinity Computer and numerical computations with infinities and in infinitesimals Abstract: The lecture presents a recent methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers on a new type of a computer – the Infinity Computer – patented in EU, USA, and Russia (see [23]). The new approach is based on the principle ‘The whole is greater than the part’ (Euclid’s Common Notion 5) that is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework different from that of the non-standard analysis [...] http://pages.di.unipi.it/fpoloni/files/seminari/Sergeyev_Infinity.pdf === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

1 0

Optimization & Numerical Analysis seminars: Sergeyev
by Federico Poloni 17 Mar '16

17 Mar '16

Speaker: Yaroslav D. Sergeyev Affiliation: Università della Calabria and N.I. Lobachevsky University of Nizhni Novgorod, Russia. Time: Monday, 11 April 2016, 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Lipschitz global optimization Abstract: Global optimization is a thriving branch of applied mathematics and an extensive literature is dedicated to it (see e.g., [1–24]). In this lecture, the global optimization problem of a multidimensional function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. It is supposed that the objective function can be “black box”, multiextremal, and non-differentiable. It is also assumed that evaluation of the objective function at a point is a time-consuming operation. Many algorithms for solving this problem have been discussed in literature. They can be distinguished, for example, by the way of obtaining information about the Lipschitz constant and by the strategy of exploration of the search domain. Different exploration techniques based on various adaptive partition strategies are analyzed. [...] http://pages.di.unipi.it/fpoloni/files/seminari/Sergeyev.pdf === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

1 0

Seminari su Mathematica
by Francesco Romani 02 Mar '16

02 Mar '16

Nell’ambito del corso di Esperienze di programmazione saranno tenuti 4 seminari introduttivi di circa 2 ore sul linguaggio Mathematica. Mercoledì 9/3 11-13 Aula C1 Introduzione a Mathematica Mercoledì 16/3 11-13 Aula C1 Grafica con Mathematica Mercoledì 23/3 11-13 Aula C1 Programmazione in Mathematica Mercoledì 27/4 11-13 Aula C1 Calcolo Numerico con Mathematica La partecipazione è aperta a tutti e vi prego di diffondere l’informazione ad eventuali interessati. Grazie, saluti, FR ____________________________ Prof. Francesco Romani Dipartimento di Informatica Via Buonarroti 2, 56127 PISA, ITALY Tel +39-050-2212734 FAX +39-050-2212726 http://www.di.unipi.it/~romani

1 0

Mathematica
by Francesco Romani 29 Feb '16

29 Feb '16

Anche quest’anno, all’interno del corso di Esperienze di Programmazione, faccio 4-5 seminari su Mathematica. L’orario è mercoledi 11-13 / Venerdi 16-18 Avendo una certra libertà per collocarli volevo sapere se qualcuno ha intenzione di seguirli e ha preferenze sugli orari. Grazie saluti Francesco ____________________________ Prof. Francesco Romani Dipartimento di Informatica Via Buonarroti 2, 56127 PISA, ITALY Tel +39-050-2212734 FAX +39-050-2212726 http://www.di.unipi.it/~romani

1 0

Optimization & Numerical Analysis seminars: Masciotta
by Federico Poloni 29 Feb '16

29 Feb '16

Speaker: Andrea Masciotta Affiliation: Dipartimento di Matematica, Università di Pisa Time: Monday, 7 March 2016, 14:30 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Minimization algorithms for compressive sensing Abstract: Compressive sensing is a new approach to digital signals acquisition and processing. Its main aim is the reconstruction of sparse signals or images (i.e. with few significant coefficients) from what was previously believed to be incomplete information. Compressive sensing has many potential applications, not only limited to the analysis of signals or images. In this talk we will first describe the main theoretical properties of compressive sensing, then three solution algorithms based on \ell_1 minimization will be presented, along with numerical experiments to highlight the main characteristics of these three methods in the framework of compressive sensing. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

1 0

Optimization & Numerical Analysis seminars: Miglierina
by Federico Poloni 17 Feb '16

17 Feb '16

Speaker: Enrico Miglierina Affiliation: Università Cattolica del Sacro Cuore, Milano Time: Thursday, 25 February 2016, 15:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: Stability by set convergences: from Vector to Set optimization Abstract: (pdf) http://pages.di.unipi.it/fpoloni/files/seminari/Miglierina.pdf The notions of set convergences reveal to be very useful to study stability properties in vector optimization. Indeed, some results that show how the convergence of feasible region implies the convergence of efficient frontiers are known. The oldest ones are based on suitable compactness assumptions that concern the sequence of sets as a whole(see \cite{Attouch-Rihai,Bednarczuk2007,Luc-Lucchetti-Malivert,LoridanMorganRaucci,Penot-Sterna}). Moreover, more recently, some results about convergence of efficient frontiers have been obtained by replacing compactness by convexity (\cite{Lucchetti-Miglierina2004Opt,MM2005}). After a presentation of these results, the last aim of the talk is to extend this class of results to the broader framework of set optimization, that recently received an increasing attention in the literature (\cite{Gutierrez-Miglierina-Molho-Novo}). === Everyone is welcome! -- --federico poloni _______________________________________________ Numpi.di mailing list Numpi.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/numpi.di

1 0

[Dipartimento.di] Reminder: Optimization & Numerical Analysis seminars: Strabic
by Federico Poloni 18 Dec '15

18 Dec '15

Speaker: Nataša Strabić Affiliation: The University of Manchester Time: Wednesday, December, 9; h. 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Recent Progress on the Nearest Correlation Matrix Problem Abstract: In a wide range of applications it is required to replace an empirically obtained unit diagonal indefinite symmetric matrix with a valid correlation matrix (unit diagonal positive semidefinite matrix). A popular replacement is the nearest correlation matrix in the Frobenius norm. The first method for computing the nearest correlation matrix with guaranteed convergence was the alternating projections method proposed by Higham in 2002. The rate of convergence of this method is at best linear, and it can require a large number of iterations to converge to within a given tolerance. Although a faster globally convergent Newton algorithm was subsequently developed by Qi and Sun in 2006, the alternating projections method remains very widely used. We show that Anderson acceleration, a technique for accelerating the convergence of fixed-point iterations, can be applied to the alternating projections method and that in practice it brings a significant reduction in both the number of iterations and the computation time. We also show that Anderson acceleration remains effective, and indeed can provide even greater improvements, when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. This is particularly significant for the nearest correlation matrix problem with fixed elements because no Newton method with guaranteed convergence is available for it. Both methods for computing the nearest correlation matrix are based on repeated eigenvalue decompositions and so they can be infeasible in time-critical situations. We have recently proposed an alternative method to restore definiteness to an indefinite matrix called shrinking. The method is based on computing the optimal parameter in a convex linear combination of the indefinite starting matrix and a chosen positive definite target matrix. We show how this problem can be solved by the bisection method and posed as a generalized eigenvalue problem, and we demonstrate how exploiting positive definiteness in these two methods leads to impressive computational savings. The work on these two topics is joint with Nicholas J. Higham, and, for shrinking, with Vedran Šego. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

2 1

[Dipartimento.di] Optimization & Numerical Analysis seminars: Strabic
by Federico Poloni 03 Dec '15

03 Dec '15

Speaker: Nataša Strabić Affiliation: The University of Manchester Time: Wednesday, December, 9; h. 15:00 Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Recent Progress on the Nearest Correlation Matrix Problem Abstract: In a wide range of applications it is required to replace an empirically obtained unit diagonal indefinite symmetric matrix with a valid correlation matrix (unit diagonal positive semidefinite matrix). A popular replacement is the nearest correlation matrix in the Frobenius norm. The first method for computing the nearest correlation matrix with guaranteed convergence was the alternating projections method proposed by Higham in 2002. The rate of convergence of this method is at best linear, and it can require a large number of iterations to converge to within a given tolerance. Although a faster globally convergent Newton algorithm was subsequently developed by Qi and Sun in 2006, the alternating projections method remains very widely used. We show that Anderson acceleration, a technique for accelerating the convergence of fixed-point iterations, can be applied to the alternating projections method and that in practice it brings a significant reduction in both the number of iterations and the computation time. We also show that Anderson acceleration remains effective, and indeed can provide even greater improvements, when it is applied to the variants of the nearest correlation matrix problem in which specified elements are fixed or a lower bound is imposed on the smallest eigenvalue. This is particularly significant for the nearest correlation matrix problem with fixed elements because no Newton method with guaranteed convergence is available for it. Both methods for computing the nearest correlation matrix are based on repeated eigenvalue decompositions and so they can be infeasible in time-critical situations. We have recently proposed an alternative method to restore definiteness to an indefinite matrix called shrinking. The method is based on computing the optimal parameter in a convex linear combination of the indefinite starting matrix and a chosen positive definite target matrix. We show how this problem can be solved by the bisection method and posed as a generalized eigenvalue problem, and we demonstrate how exploiting positive definiteness in these two methods leads to impressive computational savings. The work on these two topics is joint with Nicholas J. Higham, and, for shrinking, with Vedran Šego. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

1 0

Optimization & Numerical Analysis seminars: Fenu
by Federico Poloni 19 Nov '15

19 Nov '15

Speaker: Caterina Fenu Affiliation: Università di Pisa Time: Thursday, November, 26; 9 am Place: Sala Seminari Ovest, Dipartimento di Informatica, Università di Pisa Title: Fast Computation of Centrality Indices Abstract: One of the main issues in complex networks theory is to find the “most important” nodes. To this aim, one can use matrix functions applied to its adjacency matrix. After an introduction on the use of Gauss-type quadrature rules, we will discuss a new computational method to rank the nodes of both directed and undirected (unweighted) networks according to the values of these functions. The algorithm uses a low-rank approximation of the adjacency matrix, then Gauss quadrature is used to refine the computation. Extended pdf abstract on http://www.di.unipi.it/~fpoloni/files/seminari/Fenu.pdf === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel. +39 050 2213143

1 0

Optimization & Numerical Analysis seminars: Brugiapaglia
by Federico Poloni 23 Oct '15

23 Oct '15

Speaker: Simone Brugiapaglia Affiliation: Politecnico di Milano --- Laboratory for Modeling and Scientific Computing MOX Time: Tuesday, December 15, 11 am Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: CORSING: Sparse approximation of PDEs based on Compressed Sensing Abstract: We present a novel method for the numerical approximation of PDEs, motivated by recent developments in sparse representation, and particularly by compressed sensing. We named this approach CORSING (COmpRessed SolvING). Establishing an analogy between the sampling of a signal and the Petrov-Galerkin discretization of a PDE, the CORSING method can recover the best s-term approximation to the solution with respect to N suitable trial functions, with s<<N, by evaluating the bilinear form associated with the PDE against a randomized choice of m<<N test functions. This yields an underdetermined m x N linear system, that is solved by means of sparse optimization techniques. A theoretical analysis of the CORSING procedure is presented, based on the concepts of local a-coherence and restricted inf-sup property, along with numerical experiments that confirm the robustness and reliability of the proposed strategy. === Everyone is welcome! -- --federico poloni Dipartimento di Informatica, Università di Pisa http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

1 0